giving a 100 million dollar donation allows you to subtract 100 million from your income (assuming you had a lot more income, there is a limit) which at a 50% tax rate means you gave $50 million out of your account and the charity received $100 million into theirs, the rest coming from the govt in the form of taxes you would have given them but they didn't get from you.
non-profits accepting donations will allow you to structure them as is tax advantageous to you, say $10 million a year for 10 years, is announced as a $100 million donation.
but with appreciated assets something trickier happens. Say I paid $10 million for a block of stock, and it appreciates to $110 million. If I sell it, $100 million of that is income, but I donate the income so I don't have to pay tax on it... However, if I don't sell the stock, and just donate $100 million of it as stock, my charitable contribution is $100 million, and there is no tax on the $91 million portion which is income (did I do that arithmetic right?) and therefore I can deduct the $100 million donation from an additional $100 million of income completely unrelated to this block of stock. The US treasury and public will never see any tax for all that income, and will give me a break on the rest of my taxes.